Dicke superradiance of a two-component Fermi gas coupled to a quantized light field

We study the superradiance transition of a two-component three-dimensional Fermi gas interacting with a single-mode light field of Dicke-type coupling. We find that for a noninteracting gas, due to the Fermi blocking, a unique superradiant state with a superradiant outer shell surrounding an inner Fermi sea may appear, and the critical atom-light coupling strength $g_c$ to trigger the superradiance approaches $\sqrt{{\omega }_c{E}_F/3}$ even for a vanishing transition frequency between a two-spin state (${\omega }_a\to 0$), in contrast to $g_c\sim \sqrt{{\omega }_c{\omega }_a}\to 0$ for a bosonic or spin system. When the atom-atom attraction is included, we find that the atomic superfluid would compete with the superradiance directly and both orders cannot coexist, giving rise to an interesting ground-state phase diagram with a tricritical point. The resultant phases and phase transitions are characterized by the unique fluctuation spectrum beyond the mean-field level. We further analyze the effects caused by the decay of the light field, which is inevitable for a possible realization in a cavity with a cold atom system. Our results would be beneficial for the understanding of the interplay between Fermi superfluid and superradiance.

Figure 1

(a) The solid line shows the critical atom-light coupling strength $g_c/E_F$ as a function of atomic transition frequency ${\omega }_a/E_F$. The color bar shows the scaled photon number ${\left|\alpha \right|}^2/N$. The dashed line separates the superradiant state with ($k_{\mathrm{in}}>0$) or without ($k_{\mathrm{in}}=0$) an inner Fermi surface, which ends at a tricritical point at $({\omega }_a/E_F,g/E_F)=(1.577,0.6288)$. (b) The Fermi momentum $k_{\mathrm{in}}/k_F$ of the inner Fermi sea and the scaled superradiant order parameter $\alpha /\sqrt{N}$ as functions of the atom-light coupling strength $g/E_F$ for different ${\omega }_a/E_F=0$ (blue solid) and 1 (red dash-dotted). Here, the light field frequency ${\omega }_c/E_F=1$.

Figure 2

(a) The ground-state phase diagram in the $g\text{−}{\omega }_a$ plane at unitary regime with ${(-a_s{k}_F)}^{-1}=0$, which contains three phases: the superfluid (SF) state, the superradiant (SR) state, and the normal gas (NG); (b) the SF order parameter $\mathrm{\Delta }/E_F$ (blue solid) and the SR order parameter $\alpha /\sqrt{N}$ (red dash-dotted) as functions of scattering length ${(-a_s{k}_F)}^{-1}$. The inset shows the evolution of the chemical potential $\mu$. Other parameters are ${\omega }_c/E_F={\omega }_a/E_F=g/E_F=1$. (c) The critical coupling strength $g_c/E_F$ as a function of the scattering length ${(-a_s{k}_F)}^{-1}$ for ${\omega }_a=0$ (blue dashed) and ${\omega }_a/E_F=1$ (red solid). Here ${\omega }_c/E_F=1$.

Figure 3

Evolution of the excitation energy $E_{\mathrm{ex}}/E_F$ vs the atom-light coupling strength $g/E_F$ for two typical interaction parameters: (a) $-1/a_s{k}_F=-1$ and (b) $-1/a_s{k}_F=1$. Here, ${\omega }_c/E_F={\omega }_a/E_F=1$. There are three branches: one is of photon-type (blue dash-dotted) and two are of matter-type (green solid and red dashed).

Figure 4

The SR critical coupling strength $g_c/E_F$ as a function of ${(-a_s{k}_F)}^{-1}$ for decay rate $\kappa =0$ (red dashed), 0.5 (green dot-dashed), and 1 (blue solid). Here, ${\omega }_a=0$ and ${\omega }_c/E_F=1$.

Figure 5

The real part (a), (c) and the imaginary part (b), (d) of the excitation energy $E_{\mathrm{ex}}/E_F$ as functions of $g/E_F$ for two interaction parameters: (a), (b) $-1/a_s{k}_F=0$ and (c), (d) $-1/a_s{k}_F=1$. Here, $\kappa /E_F=1$ and other parameters are the same as in Fig. 3.